Finding std. deviation when only given interval?
I'm supposed to find the standard deviation of the interval (15, 22), and the only other information I'm given is that the distribution is uniform.
Can I do this on my ti-84?
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The probability density function of the uniform distribution is:
1/(22-15) dx
= 1/7 dx , 15 < x < 22
Mean = E(x) = (1/7) ∫ [15,22] x dx
= (1/14) x^2
Let F(x) = x^2/14
F(22) = 22^2/14
F(15)= 15^2/14
E(x) = F(22)-F(15) = 22^2/14 -15^2 /14 = (484-225)/ 14 = 18.5
E(x^2) = (1/7) ∫ [15,22] x^2 dx
= (1/7) (1/3) x^3
= (1/21) x^3
Let F(x) = (1/21) x^3
F(22) = 22^3 / 21
F(15)= 15^3 / 21
F(22)-F(15) = E(x^2) = 22^3 / 21 - 15^3 / 21 = 346.333
Variance = E(x^2) - [E(x)]^2
= 346.333 - (18.5)^2 = 4.083
Standard deviation = sqrt(4.083) = 2.0206